Young’s Modulus Measurement Using a Simplified Transparent Indenter Measurement Technique

In material nano- and micro-indentation research, it is well accepted to use the initial unloading stiffness of the load-depth curve to determine the material’s Young’s modulus. This approach requires the use of high-precision displacement sensors in order to calibrate the loading apparatus system compliance and thus obtain the load-depth curve accurately. In this research, using a transparent spherical indenter coupled with a multi-partial unloading technique, we present a simpler approach to measure the material’s Young’s modulus. Experimental results of several metallic alloys and related discussions are presented.     

An Instrumented Indentation Method for Young’s Modulus Measurement with Accuracy Estimation

The relationships between indentation responses and Young’s modulus of an indented material were investigated by employing dimensional analysis and finite element method. Three representative tip bluntness geometries were introduced to describe the shape of a real Berkovich indenter. It was demonstrated that for each of these bluntness geometries, a set of approximate indentation relationships correlating the ratio of nominal hardness/reduced Young’s modulus H _n /E _r and the ratio of elastic work/total work W _e/W can be derived. Consequently, a method for Young’s modulus measurement combined with its accuracy estimation was established on basis of these relationships. The effectiveness of this approach was verified by performing nanoindentation tests on S45C carbon steel and 6061 aluminum alloy and microindentation tests on aluminum single crystal, GCr15 bearing steel and fused silica.     

Large In-plane Deformation Mapping and Determination of Young’s Modulus of Rubber Using Scanner-Based Digital Image Correlation

Experimental Techniques - We propose a novel scanner-based digital image correlation (DIC) method to determine the full-field in-plane displacement as well as the Young’s modulus of...     

Accuracy of the Sampling Moiré Method and its Application to Deflection Measurements of Large-Scale Structures

Measuring accurate displacement distributions for large-scale structures is an important issue and a very challenging task. Recently, a simple and accurate phase measurement technique called sampling moiré method [Exp Mech 50–4:501–508, (2010)] has been developed for small-displacement distribution measurements. In this method, the phase distribution of moiré fringes can be analyzed from a single grating image by simultaneously performing down-sampling image processing and intensity-interpolation to generate multiple phase-shifted moiré fringe images. In addition, the phase of the original grating can also be obtained from the phase of the moiré fringe by adding the phase of the sampling grating. In this study, the measurement accuracy of the sampling moiré method was analyzed through computer simulations and a displacement measurement experiment. Four factors of the sampling moiré method were investigated, including the sampling pitch, the order of the intensity-interpolation, random noise, and the form of grating. The results show that determining the optimal sampling pitch is an important factor for obtaining better results but it is not critical. In addition, a practical application of the sampling moiré method is presented that involves a deflection measurement on a 10-meter-long crane. The experimental results demonstrate that submillimeter deflections of the crane can be successfully detected.     

Sampling Moiré Method for Accurate Small Deformation Distribution Measurement

In this paper, a novel accurate deformation distribution measurement technique by using sampling moiré method is proposed. The basic principle and an experimental result of a steel beam in symmetric three-point bending are reported. In this method, the measurement area of a target is attached with an adhesive tape of a known pitch grating firstly. An ordinary CCD camera is installed on a fixed point to record the image during deformation. The captured image is analyzed by performing easy image processing, i.e., thinning-out and linear interpolation, to obtain the multiple phase-shifted moiré patterns. Then, the phase distribution of the moiré pattern can be calculated using phase-shifting method. Finally, the deformation distribution is calculated by the grating pitch times the phase difference of before deformation and after deformation. The experimental results in symmetric three-point bending test show that the displacement of the steel beam at loading point agree well with those obtained by an accurate displacement sensor. The average error of displacement measurement is less than 4 μm when 2 mm grating pitch is used, and it corresponds to 1/500 of the grating pitch accuracy. This indicates that noncontact deformation distribution measurement is possible by simple and easy procedure with high accuracy, high speed, and low cost for the structural evaluation of infrastructures.     

Identification of Damping and Dynamic Young’s Modulus of a Structural Adhesive Using Radial Basis Function Neural Networks and Modal Data

In this paper, the radial basis function neural networks (RBFNN) was applied to the problem of identifying dynamic Young’s modulus and damping characteristic of a structural adhesive, using modal data. To identify Young’s modulus from undamped model, an appropriate RBFNN using modal data (mode shape and natural frequency) in each mode is developed. Based on a previous work, in order to identify loss factor, two approaches adopted in the identification process. In the first one, a two stage RBFNN is developed. In stage I, Young’s modulus is identified from undamped model and in stage II using the results of stage I an appropriate RBFNN is developed in each mode for identification of loss factor by implementing real parts of eigenvalues of damped model. In the second approach, a one stage RBFNN is developed using real and imaginary parts of eigenvalues of damped model to identify Young’s moduli and loss factors simultaneously. The repeatability and consistency of the method is proved by repeating the identification process for several times. The validity of results is proved by comparing the results with those identified in a previous work.     

Measurement of Temperature-Dependent Young’s Modulus at a Strain Rate for a Molding Compound by Nanoindentation

The mechanical properties of a molding compound on a packaged integrated circuit (IC) were measured by spherical nanoindentation using a 50 μm radius diamond tip. The molding compound is a heterogeneous material, consisting of assorted diameters of glass beads embedded in an epoxy. Statistical analysis was conducted to determine the representative volume element (RVE) size for a nanoindentation grid. Nanoindentation was made on the RVE to determine the effective viscoelastic properties. The relaxation functions were converted to temperature-dependent Young’s modulus at a given strain rate at several elevated temperatures. The Young’s modulus values at a given strain rate from nanoindentation were found to be in a good agreement with the corresponding data obtained from tensile samples at or below 90 °C. However, the values from nanoindentation were significantly lower than the data obtained from tensile samples when the temperature was near or higher than 110 °C, which is near the glass transition. The spatial distribution of the Young’s modulus at a given strain rate was determined using nanoindentation with a Berkovich tip. The spatial variation of the Young’s modulus at a given strain rate is due to the difference in nanoindentation sites (glass beads, epoxy or the interphase region). A graphical map made from an optical micrograph agrees reasonably well with the nanoindentation results.     

Micro-deformation Study of Stainless Steel Impacted by Ceramic Particle Using Electron Moiré Method

Background

High-velocity oxy-fuel (HVOF)-sprayed metallic coating can be used to create a surface layer that plays a significant role in enhancing the overall strength, stiffness, and fatigue life of the treated material. The micro-deformation around a single impacted particle is a critical factor that must be considered for the optimization of the HVOF process.

Objective

In this study, the micro-deformation field of stainless steel impacted by a ceramic particle was characterized at the micro-scale.

Method

A grid with a frequency of 1200 lines/mm was fabricated on the surface of stainless steel specimen. The microscopic deformation field formed on the substreate surface, induced by the impact of micro-particles with a diameter of 18 µm, was determined using the electron moiré method and numerical simulations.

Results

The in-plane plastic strain around the impacted particle was found to be as high as 9.1%, and the value sharply decreased with the increase of the distance to the edge of the impacted particle. The diameter of the plastic area was about 40 µm, which was approximately 2.2 times larger than the particle size. The experimental results were compared with numerical simulation results, and good agreement between the results was found.

Conclusions

The electron moiré technique can be a useful tool for the measurement of the deformation field induced by an impacted particle in a very local area with a size on the order of microns.

     

A Study of Crack–inclusion Interactions and Matrix–inclusion Debonding Using Moiré Interferometry and Finite Element Method

Failure behavior of composite materials in general and particulate composites in particular is intimately linked to interactions between a matrix crack and a second phase inclusion. In this work, surface deformations are optically mapped in the vicinity of a crack–inclusion pair using moiré interferometry. Edge cracked epoxy beams, each with a symmetrically positioned cylindrical glass inclusion ahead of the tip, are used to simulate a compliant matrix crack interacting with a stiff inclusion. Processes involving microelectronic fabrication techniques are developed for creating linear gratings in the crack–inclusion vicinity. The debond evolution between the inclusion–matrix pair is successfully mapped by recording crack opening displacements under quasi-static loading conditions. The surface deformations are analyzed to study evolution of strain fields due to crack–inclusion interactions. A numerical model based on experimental observations is also developed to simulate debonding of the inclusion from the matrix. An element stiffness deactivation method in conjunction with critical radial stress criterion is successfully demonstrated using finite element method. The proposed methodology is shown to capture the experimentally observed debonding process well.

Identification of Dynamic (Young’s and Shear) Moduli of a Structural Adhesive Using Modal Based Direct Model Updating Method

In this paper, mechanical characteristics (Young’s modulus and shear modulus) of an adhesive are identified using modal based direct model updating method and experimental modal data. The results show that both Young’s and shear moduli of adhesive are frequency dependent. Also, it is demonstrated that the thickness and length of the adhesive-line have influence on these properties. All experiments and subsequent identifications are conducted both in bending and shear modes, and it has been shown that the shear modulus of adhesive is more sensitive to length and thickness variations. The repeatability and consistency of method is proved through repeating the process several times and with different adherends.     

Measurements of Deflection and Residual Stress in Thin Films Utilizing Coherent Light Reflection/Projection Moiré Interferometry

Thin film technology is an area of great importance in current applications of opto-electronics, electronics, MEMS and computer technology. A critical issue in thin film technology is residual stresses that arise when the coating is deposited onto a substrate. Residual stresses can be very large in magnitude and have detrimental effects on the role that the thin film must play. To save development time on coating deposition processes it is important to perform accurate residual stresses measurements in situ in real time where the deposition is made. A novel optical set up is developed in this study to measure deflections and residual stresses generated in coated specimens that can be applied directly in the reactor utilized in the deposition process. Experimental results are in good agreement with other measurements carried out independently and other data reported in literature for thin films like those tested in the experiments.     

Development of Solute-solvent Separation Soft Lithography Grating for Measuring High-temperature In situ Deformation Using Scanning Electron Microscope Moiré Method

In this study, a technique is developed for fabricating high-temperature solute-solvent separation soft lithography (HSS-SL) grating for metallic materials. Using this technique, a 150 lines/mm crossing-type grating is directly fabricated on the surface of a miniaturized single edge notch tension (SENT) specimen. Further, the microstructure of the grating is analyzed using scanning electron microscope (SEM) and atom force microscope. The grating is found to be highly suited for forming high-contrast SEM moiré fringes. In addition, the chemical composition of the grating is characterized using energy dispersive X-ray spectroscope (EDS), whose results indicate that the grating exhibits good resistance to high-temperature oxidation owing to the high heat endurance of its constituent materials, SiO and SiO₂. With respect to high-temperature applications, the HSS-SL grating is employed successfully for measuring the linear thermal expansion coefficient of GH2036 alloy at temperatures of 25-600 °C. Moreover, the high-temperature displacement and strain fields around the semicircular notch of the SENT specimen are determined based on the SEM moiré. These results confirm that thus-fabricated HSS-SL gratings show high potential for use in high-temperature in situ deformation measurements using the SEM moiré method.

     

Extrema of Young’s modulus for cubic and transversely isotropic solids

For a homogeneous anisotropic and linearly elastic solid, the general expression of Young’s modulus E(n), embracing all classes that characterize the anisotropy, is given. A constrained extremum problem is then formulated for the evaluation of those directions n at which E(n) attains stationary values. Cubic and transversely isotropic symmetry classes are dealt with, and explicit solutions for such directions n are provided. For each case, relevant properties of these directions and corresponding values of the modulus are discussed as well. Results are shown in terms of suitable combinations of elements of the elastic tensor that embody the discrepancy from isotropy. On the basis of such material parameters, for cubic symmetry two classes of behavior can be distinguished and, in the case of transversely isotropic solids, the classes are found to be four. For both symmetries and for each class of behavior, some examples for real materials are shown and graphical representations of the dependence of Young’s modulus on direction n are given as well.     

High-precision and Arbitrary Arranged Projection Moiré System Based on an Iterative Calculation Model and the Self-calibration Method

Experimental Mechanics - Background As a full-field optical metrology, projection moiré approach has been widely used in many engineering applications. The modeling of moiré system and...     

Mechanical Characterization of Angle-Ply Composite Laminates by Differential Moiré Method: The Influence of Specimens' Length-to-Width Ratio

The influence exerted by the specimen proportions on the measured performance of angle-ply [+45°/–45°]_s composite laminates is studied. Three kinds of specimens are considered, having different length-to-width ratios, made with glass/epoxy unidirectional or fabric laminae. The static tensile characteristics are measured by means of load cells, electric strain gauges and through the Moiré fringes method. The strain fields are analysed and the effects of stress concentration at the laminate-free edges are evaluated, as well as their influence on the strain distribution and the measured strength and stiffness. The results are summarized as diagrams of ultimate load and elastic modulus versus length-to-width ratio of the different specimens investigated. These diagrams allow the designer to evaluate the influence exerted by specimen proportions on the measured performance, as well as to compare characteristics which are heterogeneous, as obtained with different kinds of specimen.     

Mechanical Characterization of Biological Membranes with Moiré Techniques and Multi-Point Simulated Annealing

This paper describes an hybrid procedure for mechanical characterization of biological membranes. The in-plane displacement field of a glutaraldehyde treated bovine pericardium patch obtained with an equi-biaxial tension test is measured with intrinsic moiré and then compared with finite element predictions. Preliminary analysis of moiré patterns observed in the experiments justifies the assumption of the constitutive model based on transversely isotropic hyperelasticity. In order to determine the 16 hyperelastic constants included in the constitutive model and the fiber orientation, the difference Ω between displacement values measured with moiré and their counterpart determined numerically is minimized by means of multi-level and multi-point simulated annealing. Results clearly demonstrate the efficiency of the identification procedure presented in this research: in fact, residual difference between experimental data and numerical values of in-plane displacements is less than 2%. In order to validate the entire identification process, another experimental test is conducted by inflating the same specimen. Out-of-plane displacements, now measured with projection moiré, are compared with predictions of a new finite element model reproducing the experimental test. The 16 hyper-elastic constants previously determined are given in input to the inflation test FE model. Remarkably, experimental and numerical results are again in excellent agreement: maximum percent error on w-displacement is less than 3%.     

Optimum Young��s Modulus of a Homogeneous Cylinder Energetically Equivalent to a Functionally Graded Cylinder

For a functionally graded (FG) circular cylinder loaded by uniform pressures on the inner and the outer surfaces and Young??s modulus varying in the radial direction, we find lower and upper bounds for Young??s modulus of the energetically equivalent homogeneous cylinder. That is, the strain energies of the FG and the homogeneous cylinders are equal to each other. For a typical power law variation of Young??s modulus in the FG cylinder, it is shown that taking only two series terms, yields good values for bounds of the equivalent modulus. We also study two inverse problems. First, an investigation is made to find the radial variation of Young??s modulus in the FG cylinder, having a constant Poisson??s ratio, that gives the maximum value of the equivalent modulus. Second, the complementary problem of finding the radial variation of Poisson??s ratio in the FG cylinder, having a constant stiffness, that gives the maximum value of the equivalent modulus, is considered. It is found that the spatial variation of the elastic properties, that maximizes the equivalent modulus, depends strongly upon the external loading on the cylinder.     

A Novel Method for Gas–Water Relative Permeability Measurement of Coal Using NMR Relaxation

Using the conventional volumetric method in unsteady-state relative permeability measurements for unconventional gas reservoirs, such as coal and gas shale, is a significant challenge because the movable water volume in coal or shale is too small to be detected. Moreover, the dead volume in the measurement system adds extra inaccuracy to the displaced water determination. In this study, a low-field nuclear magnetic resonance (NMR) spectrometer was introduced into a custom-built relative permeability measurement apparatus, and a new method was developed to accurately quantify the displaced water, avoiding the drawback of the dead volume. The changes of water in the coal matrix and cleats were monitored during the unsteady-state displacement experiments. Relative permeability curves for two Chinese anthracite and bituminous coals were obtained, matching the existing research results from the Chinese coalbed methane area. Moreover, the influences of confining pressure on the shape of the relative permeability curve were evaluated. Although uncertainties and limits exist, the NMR-based method is a practical and applicable method to evaluate the gas/water relative permeability of ultra-low permeability rocks.